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Article . 2008 . Peer-reviewed
License: Wiley Online Library User Agreement
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Article . 2008
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Article . 2008
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On super connectivity of Cartesian product graphs

Authors: Min Lü; Chao Wu; Guo-Liang Chen 0001; Cheng Lv;

On super connectivity of Cartesian product graphs

Abstract

AbstractThe super connectivity κ1 of a connected graph G is the minimum number of vertices whose deletion results in a disconnected graph without isolated vertices; this is a more refined index than the connectivity parameter κ. This article provides bounds for the super connectivity κ1 of the Cartesian product of two connected graphs, and thus generalizes the main result of Shieh on the super connectedness of the Cartesian product of two regular graphs with maximum connectivity. Particularly, we determine that κ1(Km × Kn) = min{m + 2n − 4, 2m + n − 4} for m + n ≥ 6 and state sufficient conditions to guarantee κ1(K2 × G) = 2κ(G). As a consequence, we immediately obtain the super connectivity of the n‐cube for n ≥ 3. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

Related Organizations
Keywords

Connectivity, Extremal problems in graph theory, maximally connected graphs, Cartesian product, super connectivity, super connected graphs

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Top 10%
Top 10%
Average
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